A 1997 article in The New York Times discussed how long it would take for Bill Gates, the world’s second richest person at the time (behind the Sultan of Brunei), to become the world’s first trillionaire. His birthday is October 28, 1955, and on July $16,1997,$ he was worth $\$ 42$ billion. (Note: A trillion dollars is 1000 billion dollars.) Source: The New York Times.
a. Assume that Bill Gates's fortune grows at an annual rate of $58 \%,$ the historical growth rate through 1997 of Microsoft stock, which made up most of his wealth in $1997 .$ Find the age at which he becomes a trillionaire. (Hint: Use the formula for interest compounded annually, $A=P(1+i)^{n},$ with $P=42$ . Graph the future value as a function of $n$ on a graphing calculator, and find where the graph crosses the line $y=1000$ .)
b. Repeat part a using 10.5$\%$ growth, the average return on all stocks since $1926 .$ Source: CNN.
c. What rate of growth would be necessary for Bill Gates to become a trillionaire by the time is eligible for Social Security on January $1,2022,$ after he has turned 66$?$
d. Forbes magazine's listings of billionaires for 2006 and 2010 have given Bill Gates's worth as roughly $\$ 50.0$ billion and $\$ 53.0$ billion, respectively. What was the rate of growth of his wealth between 2006 and 2010$?$ Source: Forbes.